Optimal sensor placement is used to establish the optimal sensor quantity and layout. In this study, the minimum quantity and locations of measurement sensors were assumed to satisfy the constraint conditions of the optimal sensor placement. A set of strain data in a truss structure was expanded to another set of displacements corresponding to the entire degrees of freedom from the relationship between the strain and displacement. It indicates to reduce the number of sensors because the strain depends on the displacements in a finite element model. The damaged truss element was traced using the expanded data that satisfied the prescribed constraints. The proposed optimal sensor placement method has a merit to explicitly determine the optimal sensor locations without any numerical scheme and statistical methods. The method was applied to the damage detection of a single-damaged truss structure. It was shown that the optimal sensor placement method depended on the sensor layout irrespective of the same quantity of sensors. In addition, a numerical example was used to compare sensitivities to damage detection based on the sensor placement and the existence of external noise contained in the measurement data.

最佳传感器放置用于建立最佳传感器数量和布局。在这项研究中，假定最小数量和位置的测量传感器满足最佳传感器放置的约束条件。桁架结构中的一组应变数据被扩展为另一组位移，这些位移与从应变和位移之间的关系的整个自由度相对应。它表示减少传感器的数量，因为应变取决于有限元模型中的位移。使用满足规定约束条件的扩展数据跟踪受损的桁架单元。所提出的最佳传感器放置方法具有无需任何数值方案和统计方法即可显式确定最佳传感器位置的优点。该方法应用于单损伤桁架结构的损伤检测。结果表明，最佳传感器放置方法取决于传感器布局，而与相同数量的传感器无关。另外，使用一个数值示例来比较基于传感器位置和测量数据中包含的外部噪声的存在对损坏检测的敏感性。